Capillary fracture of soft gels

A liquid droplet resting on a soft gel substrate can deform that substrate to the point of material failure, whereby fractures develop on the gel surface that propagate outwards from the contact line in a starburst pattern. In this paper, we characterize (i) the initiation process, in which the number of arms in the starburst is controlled by the ratio of the surface tension contrast to the gel's elastic modulus, and (ii) the propagation dynamics showing that once fractures are initiated they propagate with a universal power law L proportional to t(3/4). We develop a model for crack initiation by treating the gel as a linear elastic solid and computing the deformations within the substrate from the liquid-solid wetting forces. The elastic solution shows that both the location and the magnitude of the wetting forces are critical in providing a quantitative prediction for the number of fractures and, hence, an interpretation of the initiation of capillary fractures. This solution also reveals that the depth of the gel is an important factor in the fracture process, as it can help mitigate large surface tractions; this finding is confirmed with experiments. We then develop a model for crack propagation by considering the transport of an inviscid fluid into the fracture tip of an incompressible material and find that a simple energy-conservation argument can explain the observed material-independent power law. We compare predictions for both linear elastic and neo-Hookean solids, finding that the latter better explains the observed exponent.